There are some fossil deposits in Northern Illinois. This one is off I-55 between I-80 & US-24. Continue down 55 toward St. Louis and visit the Cahokia Mounds.
How far west are you planning on getting? One really cool Nevada site is the Berlin-Ichthyosaur, which in addition to the eponymous marine reptile fossils, has a cool ghost town with a short underground mine tour. That’s pretty much in the center of Nevada though.
Or if you’re heading up north further east, the House Range in western Utah is famous for trilobites. There’s some commercial U-dig-it quarries, but the whole area is mostly public land so if you can figure out the right formation you’re looking for you can pretty much head up to the hills anywhere. (You’re allowed to collect invertebrate fossils on BLM land.)
On the more dinosaur-y end of things there’s of course Dinosaur National Monument which is in the northwestern corner of Colorado which could be on the way to Yellowstone. If you come up from the southwest through Helper, Utah, there’s also the Book Cliffs which if you ever had to take a class that involved sequence stratigraphy will seem very familiar. Also north of Yellowstone, there’s the Museum of the Rockies in Bozeman which has a pretty spectacular dinosaur collection.
Also, if you end up diverting off of I-90 to see the Black Hills, there’s a very cool mammoth dig site/museum in Hot Springs, South Dakota.
My stomping grounds are more north of your route, but I can check the thread if I can think of any other rock-centric stuff along whichever route you settle on!
I should have mentioned that not too far past Billings, MT is Pompey’s Pillar, which was named such by William Clark (of Lewis & Clark) after Charbonneau’s son, Jean Baptiste, who Clark called ‘Pompey’. It’s just off of I-94, so you’d have to backtrack to pick up I-90. It’s an easy hike to the top and you can see where Clark signed his name and some nice views of the Missouri River.
Chief Joseph hi way in MT is not to be missed. Check with MTDot for open and closing dates.
Add to UT sights: Cedar Breaks NM. Beautiful drive and on the way to Bryce NP.
Skip Vegas.
Seconding the I-90 route. We did Custer-Devils Tower-Black Hills-Mount Rushmore-Wall Drug-Badlands-Corn Palace several years ago. It was an extraordinary experience with quite a few slices of Americana. Yellowstone, though, stole the show, and made I-90 feel like the detour 
I put a few pictures here.
All of Utah’s “Mighty 5” national parks are pretty awesome, but I absolutely loved Bryce Canyon & Canyonlands. Just spectacularly gorgeous.
We visited both in 2010 (we stayed in Kanab, UT per suggestions from the Dope) and did day trips to Bryce, Zion, and the North Rim of the Grand Canyon. I liked Zion better as far as accessibility - the hiking (such as we did) was easier, and there’s plenty of places to find shade, as well as numerous places to dip your toes in the river. At the uppermost end of is an area where lots of people play in the water - it was a great end to the day. Hint though: if you’re not staying in the park, be on the roads well before dark. The most direct approach from Kanab is tricky in the daytime and when we were there, closed completely after 8 PM or so. We could have gotten through it but opted to go out another park entrance, to the south, and get dinner / groceries there - but the drive back to Kanab from there was close to 2 hours, along good but utterly deserted 2-lane roads, and fairly winding to be driving at night. The shorter route might also be an issue if you’ve got a moving truck: there are restrictions on the height of vehicles and some RVs have to get a special pass because they have to close down the road to other travel for a few minutes to let you through.
Bryce is utterly stunning and also a must-see. When we went, I was dealing with a knee injury and there weren’t many trails I could hike along. It seemed hotter there but that may just be my poor memory.
If you swing by Las Vegas - which you could miss entirely and not lose out - visit Valley of Fire state park a bit northeast of it. That’s where we a) learned that a rental car’s A/C really can compete with 115+ degree heat, and b) what food feels like in a convection oven (hint: when it’s 115, and a breeze crops up, it just cooks you that much faster).
Page, AZ is home to the Glen Canyon Dam and Lake Powell. There is a smoothwater rafting company that puts into the river just below the dam, and you float downstream for 3-4 hours. You get out at Lees Ferry, AZ (which is the last place vehicles can drive to the Colorado, and where lots of the whitewater trips put in) and bus back to Page. You’ve only gone about 15 river miles but the drive back is well over an hour. We loved it. Bring sunscreen, and be prepared to freeze when you have a stop and try to take a dip in the river (the water comes from the bottom of Lake Powell and has not been sun-warmed!!).
Also near Page: there is a place where you can drive and park and go for a swim in Lake Powell. We actually had to cross back to Utah to get to it. And the parking area is not remotely paved - it’s all sand, and your car CAN get stuck (thank heavens for a group of teenagers who helped push our car out of the soft spot we got stuck in). The water there was plenty warm enough to swim in.
Hotels in Page are crappy and overpriced. We stayed at an America’s Worst Value Inn and it was the dumpiest place I’ve ever stayed.
If you visit the North Rim: it’s pretty remote., and not well traveled, so much less crowded than the more touristy South Rim. I don’t know who your cell carrier is, but if you use Verizon, you will be able to use your phone there… we got a robocall while overlooking a breathtaking vista (no, thanks, I don’t think I’ll make it to the school book fair tomorrow…)
In that part of the country, don’t let your gas tank get much below half full - exits and towns can be pretty far apart.
Highway 12 (between Capital Reef and Bryce) is what I came here to mention. The only problem is that you have to keep both eyes on the winding road, so can’t enjoy the magnificent scenery.
But don’t miss Bryce and Arches . . . especially if you have a geology background.
Stay on 70 out of Columbus, pick up 78 in Pennsylvania, then PA 611 via Cedarville Road at Easton, and stop by Bucks County to bang on some rocks.
Here’s a really good thing to do in Yellowstone Park:
Find a small parking lot just east of Rte 89, about 2 miles south of the Park’s north entrance. The entrance to this lot is about 200’ south of a bridge across the Gardiner River. (You can find it in GoogleEarth with these coordinates: 44.9928 / -110.6926)
Park in the lot, grab your swimsuit & towel, and walk south about half a mile along a good path that follows the west bank of the river. This brings you to a place (44.9858 / -110.6895) where the outflow of a hot spring (very hot water) flows into the cold Gardiner River. You can swim here, finding just the temperature you’d like in the area where the two flows mingle.
This is a popular spot with locals. Park rules permit swimming here, but it’s said that the Rangers will never tell you about this place.
Disclaimer: I last did this about 5 years ago, and Yellowstone thermal flows are notoriously variable.
His mother is a trifle more famous than his father.
Here’s an interesting item worth a look in southern Utah: Pando the world’s largest - and possibly oldest - living organism.
It’s a large grove of aspen trees that continue to spring from one root system. The young estimate of its age is 80,000 years (some say it’s half a million, or more).
I was going to mention this. It’s a pretty fascinating site.
(Tangent) I used to drive between Ohio and Missouri on I70 several times a year. And there was always construction at Terre Haute. I’d be zipping along just fine, then, whammo! One-lane traffic. For years! It was like they used that stretch of highway to train the civil engineers at Rose Hulman or something.
Certainly. Your point being?
Tripler will certainly have many ideas for you, he’s been on similar routes for similar reasons more times than I can count; I’ve only been along for half of them, maybe. Plus I can summon him from hundreds of miles away…
Btw, seconding whomever said So. Utah can be hellishly hot in the summer; but if you plan ahead w/ water and shade and taking it easy you can still enjoy yourself.